135,600

2⁴ × 3 × 5² × 113

For 135,600, the 60 positive divisors have a total of 438,216. Removing 135,600 leaves 302,616, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^2 × 113

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 438,216

Proper Divisor Sum 302,616

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #135599 ← → #135601

Radix Representation

Decimal	135600
Binary	100001000110110000 (18 bits)
Octal	0o410660
Hexadecimal	0x211B0

Divisor Catalog (60)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 40 48 50 60 75 80 100 113 120 150 200 226 240 300 339 400 452 565 600 678 904 1,130 1,200 1,356 1,695 1,808 2,260 2,712 2,825 3,390 4,520 5,424 5,650 6,780 8,475 9,040 11,300 13,560 16,950 22,600 27,120 33,900 45,200 67,800 135,600

Collatz Trajectory (113 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

135,600 67,800 33,900 16,950 8,475 25,426 12,713 38,140 19,070 9,535 28,606 14,303 42,910 21,455 64,366 32,183 96,550 48,275 144,826 72,413 217,240 108,620 54,310 27,155 81,466 40,733 122,200 61,100 30,550 15,275 45,826 22,913 68,740 34,370 17,185 51,556 25,778 12,889 38,668 19,334 9,667 29,002 14,501 43,504 21,752 10,876 5,438 2,719 8,158 4,079 12,238 6,119 18,358 9,179 27,538 13,769 41,308 20,654 10,327 30,982

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